On the Local-Global Conjecture for integral Apollonian gaskets — mentioned by svat

Thu, 10 Aug 2023 17:01:12 GMT

That the curvatures are integers is proved (noticed by Soddy in 1936 as "a fairly straightforward consequence of Descartes’ equation", as the article mentions), and a lot more is also proved about the integers' distribution; the conjecture specifically is about whether every sufficiently large “admissible (passing local obstructions) integer is the curvature of some circle in the gasket” — see the second page of https://arxiv.org/abs/1205.4416, or indeed the second page of the paper the article is about (https://arxiv.org/abs/2307.02749), which puts it even more concretely: > Conjecture 1.1…

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On the Local-Global Conjecture for integral Apollonian gaskets · HackerPapers discussions

On the Local-Global Conjecture for integral Apollonian gaskets — mentioned by svat